1 / 11

1. Read the problem, pull out essential information and identify a formula to be used.

3.10 – Related Rates. Related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. . 1. Read the problem, pull out essential information and identify a formula to be used.

kioko
Télécharger la présentation

1. Read the problem, pull out essential information and identify a formula to be used.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3.10 – Related Rates Related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.  1. Read the problem, pull out essential information and identify a formula to be used. 2. Sketch a diagram if possible. 3. Write down any known rate of change & the rate of change you are looking for. 4. Be careful with signs…if the amount is decreasing, the rate of change is negative. 5. Pay attention to whether quantities are constant or varying. 6. Set up an equation involving the appropriate quantities. 7. Differentiate with respect to t using implicit differentiation. 8. Plug in known items (you may need to find some quantities using geometry). 9. Solve for the item you are looking for, most often this will be a rate of change. 10. State your final answer with the appropriate units.

  2. 3.10 – Related Rates Related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.  Example

  3. 3.10 – Related Rates Example

  4. 3.10 – Related Rates Example 3) The radius r and the height h of a right circular cone are related to the cone’s volume V by the equation How is related to if r is constant? How is related to if h is constant? How is related to if h and r are not constant?

  5. 3.10 – Related Rates 4) An oil tanker strikes an iceberg and a hole is ripped open on its side. Oil is leaking out in a near circular shape. The radius of the oil spill is changing at a rate of 1.5 miles per hour. How fast is the area of the oil spill changing when the radius is 0.6 mile?

  6. 3.10 – Related Rates 5) A balloon is being inflated at a rate of 10 cubic centimeters per second. How fast is the radius of a spherical balloon changing at the instant the radius is 5 centimeters?

  7. 3.10 – Related Rates 6) A water authority is filling an inverted conical water storage tower at a rate of 9 cubic feet per minute. The height of the tank is 80 feet and the radius at the top is 40 feet. How fast is the water level inside the tank changing when the water level is 60 feet deep? 40 ft r 80 ft

  8. 3.10 – Related Rates 7) A 25-foot ladder is leaning against a wall. The bottom of the ladder is being pulled away from the wall at a rate of 3 feet per second. How fast is the top of the ladder moving at the instant the bottom of the ladder is 15 feet away from the wall?

  9. 3.10 – Related Rates 8) A 25-foot ladder is leaning against a wall. The bottom of the ladder is being pulled away from the wall at a rate of 3 feet per second. How fast is the top of the ladder moving at the instant the bottom of the ladder is 15 feet away from the wall? At the same instant, what is the rate of change of the area between the ground, the wall, and the ladder?

  10. 3.10 – Related Rates 9) A 25-foot ladder is leaning against a wall. The bottom of the ladder is being pulled away from the wall at a rate of 3 feet per second. How fast is the top of the ladder moving at the instant the bottom of the ladder is 15 feet away from the wall? At the same instant, what is the rate of change of the angle () between the ground and the ladder?

  11. 3.10 – Related Rates

More Related